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Worksheet: Solving Proportions

Q1:

Given that π‘₯ + 𝑦 1 4 = 𝑦 + 𝑒 1 0 = 𝑒 + π‘₯ 4 , find the value of the missing denominator in the equation π‘₯ βˆ’ 𝑒 4 = 𝑦 βˆ’ π‘₯ β‹― .

Q2:

Find the number that should be added to each of the numbers 32, 9, 22, and 4 to make them proportional.

Q3:

Find the number that should be added to each of the numbers 36, 13, 14, and 2 to make them proportional.

Q4:

Find the number that should be added to each of the numbers 39, 37, 17, and 16 to make them proportional.

Q5:

Two values are in the ratio 5 ∢ 1 2 . If I add a certain number to each value, the ratio changes to 2 3 ∢ 2 4 . What is that number?

Q6:

Find the third proportional to 3, 33, and 11.

Q7:

Determine the fourth proportional of the numbers 8, 36, and 46.

Q8:

Given that 19, 8, 4 3 4 , π‘₯ are proportional, what is the value of π‘₯ ?

  • A19
  • B1.68
  • C32
  • D2

Q9:

Find an expression for the fourth proportional of the quantities ( π‘Ž βˆ’ 𝑏 ) , ( π‘Ž + 𝑏 ) , and ( π‘Ž + 𝑏 ) .

  • A ( π‘Ž βˆ’ 𝑏 ) ( π‘Ž + 𝑏 ) 2
  • B ( π‘Ž + 𝑏 ) ( π‘Ž βˆ’ 𝑏 ) 2
  • C ( π‘Ž + 𝑏 ) ( π‘Ž βˆ’ 𝑏 ) 2 2
  • D ( π‘Ž + 𝑏 ) ( π‘Ž βˆ’ 𝑏 ) 2
  • E ( π‘Ž + 𝑏 ) ( π‘Ž βˆ’ 𝑏 ) 2 2

Q10:

What is the value of π‘₯ if 3, π‘₯ + 6 , 4, and 44 are in proportion?

  • A39
  • B33
  • C126
  • D27

Q11:

What is the value of π‘₯ if 4, π‘₯ + 6 , 6, and 12 are in proportion?

  • A14
  • B8
  • C42
  • D2

Q12:

If π‘Ž , 𝑏 , 𝑐 , and 𝑑 are proportional quantities, then 𝑐 is called .

  • Athe first proportional
  • Bthe second proportional
  • Cthe fourth proportional
  • Dthe third proportional

Q13:

Find the value of π‘₯ that makes the numbers 9 3 5 , π‘₯ , 4.8, and 3.8 proportional.

Q14:

Complete the following quantities with the third proportional: π‘Ž , π‘Ž + 𝑏 , , π‘Ž βˆ’ 𝑏 2 2 .

  • A π‘Ž βˆ’ 𝑏 π‘Ž
  • B π‘Ž π‘Ž βˆ’ 𝑏
  • C π‘Ž ο€Ή π‘Ž βˆ’ 𝑏  2 2
  • D π‘Ž ( π‘Ž βˆ’ 𝑏 )

Q15:

Find an expression for the fourth proportional of the quantities ( π‘Ž + 𝑏 ) , ( π‘Ž βˆ’ 𝑏 ) , and ( π‘Ž βˆ’ 𝑏 ) .

  • A ( π‘Ž + 𝑏 ) ( π‘Ž βˆ’ 𝑏 ) 2
  • B ( π‘Ž βˆ’ 𝑏 ) ( π‘Ž + 𝑏 ) 2
  • C ( π‘Ž βˆ’ 𝑏 ) ( π‘Ž + 𝑏 ) 2 2
  • D ( π‘Ž βˆ’ 𝑏 ) ( π‘Ž + 𝑏 ) 2
  • E ( π‘Ž βˆ’ 𝑏 ) ( π‘Ž + 𝑏 ) 2 2